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A Differential Analog of the Noether Normalization Lemma.
- Source :
-
IMRN: International Mathematics Research Notices . Feb2018, Vol. 2018 Issue 4, p1177-1199. 23p. - Publication Year :
- 2018
-
Abstract
- In this paper, we prove the following differential analog of the Noether normalization lemma: for every d-dimensional differential algebraic variety over differentially closed field of zero characteristic there exists a surjective map on to the d-dimensional affine space. Equivalently, for every integral differential algebra A over differential field of zero characteristic there exist differentially independent b1, . . . , bd such that A is differentially algebraic over subalgebra B differentially generated by b1, . . . , bd, and whenever p ⊂ B is a prime differential ideal, there exists a prime differential ideal q ⊂ A such that p = B ∩ q. We also prove the analogous theorem for differential algebraic varieties over the ring of formal power series over an algebraically closed differential field and present some applications to differential equations. [ABSTRACT FROM AUTHOR]
- Subjects :
- *NOETHER'S theorem
*ALGEBRA
*CONSERVATION laws (Mathematics)
*MATHEMATICS
*EQUATIONS
Subjects
Details
- Language :
- English
- ISSN :
- 10737928
- Volume :
- 2018
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- IMRN: International Mathematics Research Notices
- Publication Type :
- Academic Journal
- Accession number :
- 128157788
- Full Text :
- https://doi.org/10.1093/imrn/rnw275